论文标题
在e型K理论中的适当动作和分解
Proper actions and decompositions in equivariant K-theory
论文作者
论文摘要
在本文中，我们研究了$ g $ equivariant $ k $的自然分解，当时$ g $ - 空间的理论是$ g $时，当$ g $是一个带有紧凑的普通亚组$ a $的谎言组时。我们的分解可以理解为在适当假设下称为Mackey机器的理论的概括，因为它在扭曲的epivariant K理论组方面分解了$ g $ equivariant K理论。类似的分解以作用于空间的紧凑型谎言组而闻名，但我们的主要结果适用于离散，线性和几乎连接的组。我们还应用这种分解来研究仅具有一种各向同性类型的空间的模棱两可的$ k $。我们提供了丰富的示例，以揭示结果的力量和普遍性。我们还根据第三作者发表的以前的论文，研究了对等效结缔组织的分解$ k $ - $ k $ hymology for紧凑型谎言组的动作。
In this paper we study a natural decomposition of $G$-equivariant $K$-theory of a proper $G$-space, when $G$ is a Lie group with a compact normal subgroup $A$ acting trivially. Our decomposition could be understood as a generalization of the theory known as Mackey machine under suitable hypotheses, since it decomposes $G$-equivariant K-theory in terms of twisted equivariant K-theory groups respect to some subgroups of $G/A$. Similar decompositions were known for the case of a compact Lie group acting on a space, but our main result applies to discrete, linear and almost connected groups. We also apply this decomposition to study equivariant $K$-theory of spaces with only one isotropy type. We provide a rich class of examples in order to expose the strength and generality of our results. We also study the decomposition for equivariant connective $K$-homology for actions of compact Lie groups using a suitable configuration space model, based on previous papers published by the third author.
